Would Nixon have won in '60 had there been no voter fraud?

[Kingpoleon]

And, of course, Kennedy probably would have won states like Mississippi, Florida, and Virginia if African Americans weren't being systematically disenfranchised. 

I could be wrong about this (and please correct me if I am), but weren't Southern blacks still opposed to the Democratic Party until 1964?

I don't think they were "unopposed" after either, but they saw the national Democratic Party as a (barely) better vehicle for their interests than the national Republican Party.  In most of the Deep South, Blacks had a choice between a racist party that fought for poor people or a racist party that fought for rich people.

Winthrop Rockefeller.